Hi Steven and Merry Christmas to you too.
If the provider is providing you an Ethernet connection, then you can use the 3560g you have and as you already know you can use it as a layer-3 device. But, if the provider is giving you anything else, i.e. T1, T3, DSL, etc... then you need a router with proper WIC to terminate the connection, because the 3560 supports only Ethernet. If you are planning to run BGP, OSPF on your 3560, you need to make sure you have the proper later-3 image. (IP services).
Also, if you are doing NAT, you need a router.
HTH
Reza